I'm going to give some information on methodology in this field for the late 16th century and early 17th century in Germany, both reliable and unreliable.
The most reliable methods for ascertaining how widely village schools were distributed in Germany for, say, the period from 1530-1630, has to be done individual territory by individual territory (not all started at the same time and some only had school in spurts, depending on the views of who had the cuius regio at the moment). The Kirchenordnung and its provisions give a place to start -- this at least indicates what the individual Landesherr and his bureaucrats were hoping to achieve and what instructions were being given to local ecclesiastical officials, to town councils, and to village Gemeinden, since all of those were involved in implementation.
Then the actual records need to be triangulated. The triangulation uses three approaches:
(1) minutes of the church consistories, district by district, to see how many people presented themselves as candidates, how many were approved, and to which parishes they were nominated;
(2) budget records of individual parishes with each church district to see how many of them were paying teachers, whether the teacher(s) were full-time or part-time; and, if part time, what other job in the parish they were sharing;
(3) in chartered towns and cities, minutes and budget records of the civil authorities to see what provisions and actual payments were made for what kind of school buildings.
The above can be supplemented by a variety of other types of record.
High upon the list are records of endowments in those territories such as Wuerttemberg in which the Lutheran rulers had not "secularized" the medieval church properties in the sense we're most familiar with in England, but rather had turned them into endowments for the university, the library, the seminaries, the Latin Schools, and other institutions that he considered crucial to the support of his administration. The Latin School records are particularly important in that they usually record the school background of all the admitted students (who came in, ordinarily, at about age 10), indicating g the village school, the nominating pastor, the ability of the family to pay all or part of the fees, etc.
Also valuable are the many ecclesiastical visitation records. These were not done on a basis of "every 10 years" or at the same time in every individual territory. However, most territories have several during the century from 1530-1630. These were not superficial. They started with a written questionnaire sent out by the central administration of the church in the territory (be it Lutheran, Calvinist, or Catholic). This was followed up by a team of inspectors, which (answered or unanswered questionnaire in hand) hit every single parish, interviewed the employees, interviewed the village council, interviewed individuals, and recorded the results. These guys were congenital pessimists. They did not cast a rosy glow over anything. They believed sincerely in original sin and individual depravity. They were happy to record every complaint about a school -- absent, held only sporadically, held only in the morning, the building in bad condition, the teacher too inclined to drink, the teacher too inclined to flirt with the sexton's wife, not enough catechisms, not enough other books. You name the transgression -- they did their best to catch it.
For the Thirty Year War immediate period, those ecclesiastical visitation records can be supplemented by the visitations done by the various secular administrations, such as that in Hessen-Kassel in 1636-1637, that were designed to evaluate how much of the infrastructure had been destroyed by military activity and what it was likely to cost to rebuild it. Here, again, the villages were, if anything, inclined to exaggerate their reports of how bad things were, since they were all, all, hoping for a rebate of their tax obligations on the grounds that "the roof had burned off the school building and would have to be replaced, the teacher was gone and they would have to find somebody else," etc.
In central Germany and most of the Rhineland, grades 1-4 schools were pretty well universally available by 1600 and were conducted at least several months of the year. The **real difference** between this part of Germany and any comparison with the US prior to 1820 is the different settlement patterns. The American colonies mostly developed with dispersed individual farms. In early modern Germany, also, the lowest rates of schooling were found in areas of dispersed settlement. Prosperity didn't make much difference: rural schools were rare in prosperous Osnabrueck just as much as in the impoverished Bayerischer Wald, simply because it was difficult to get the kids there. (For France in the same period, Goubert points out that village schools were much commoner in those regions where the climate meant that there wasn't a lot of winter field work, and rare in those regions of the south where the climate required that irrigation installations, etc. be serviced all year round. Or, as he put it, "The Vosges produced schoolmasters at about as high a rate as the rest of F France produced shoemakers.")
The absolutely worst method of gauging early modern literacy is the "signatures in registers" method. This is for several reasons.
I've already mentioned that for technological reasons, writing with quill pen and carbon powder ink wasn't taught in the lower grades. By the late 19th and 20th centuries, reading and writing were taught together and many of the first scholars who explored this issue just didn't stop to think.
This "technology of learning" change is not unique. When I was in elementary school, still, typewriters were manual, the keys were in stepped rows, handling them took a certain strength and size of hand, and typing was not, not, ever, an elementary school subject. My mother finished 8th grade and learned to type in a year of private "business school" (paid by parental school) that came next. I learned to type as a junior in high school, and that was the year to which typing was assigned. My grandchildren are learning to type in kindergarten, now, because it's become an essential need for using computers and the keyboards are so different.
Additionally, careful study that follows a wide sample of early modern individuals throughout their lifetimes indicates that signing a document or using a mark was not consistent. Sometimes the same individual signed; sometimes he or she didn't; "not signing" doesn't seem to be a result of being ill or feeble as a result of advancing age. Indeed, in many cases in the 16th century, there's a pattern that seems to fall out -- the more important the legal document, the more likely the person (even an ordinary person with no coat of arms) was to try to draw something that resembled a legal seal rather than to write out a signature.
The French Canadians (an ethnic group which has produced millions of descendants of a manageably small group of ancestors) have done some very thorough studies of signatures in registers, both ecclesiastical and notarial, and including witnesses and "those present" and "also here to observe" as well as the parties to the transaction. This has confirmed the basic accuracy of the German studies -- that even members of the nobility with a flourishing ability to write their names sometimes, for no known reason, made a mark.